Lift and Drag on an Airfoil
ME 123: Mechanical Engineering Laboratory II: Fluids
Dr. J. M. Meyers | Dr. D. G. Fletcher | Dr. Y. Dubief
1. Introduction
In this lab the characteristics of airfoil lift, drag, and stall due to flow separation will be investigated.
Bear in mind that airfoils are not only useful for aircraft. The investigation described herein applies to
many fluid dynamic scenarios: wings on F1 cars, helicopter blades, propeller blades, hydrofoils, and wind
turbine blades are just some examples.
Lab Objectives:
• Understand the principles of Lift and Drag on an aerodynamic surface
• Acquire a pressure distribution over a body and use it to approximate Lift and Drag
• Understand the importance non-dimensional parameters of , , and
• Understand the behavior of flow separation
• Understand how flow separation behavior leads to stall (loss of lift)
Four main forces act on an aircraft in flight: Thrust (if the aircraft is powered), Drag, Lift, and Weight
(left side of Figure 1). We are concerned only with Lift and Drag at the moment. The main contribution
to lift (and substantial drag at times) comes from the wing which has a certain airfoil shape or airfoil
section (right side of Figure 1). Airfoils shapes are designed to provide high Lift values at low Drag for
given flight conditions. Conventional aircraft wings often use moving surfaces (flaps and slats) to adapt
to different conditions however our study will just focus on baseline airfoil shape.
Figure 1: Coefficient pressure distribution over an airfoil
Airfoils have a leading edge and a trailing edge, and are usually designed with different top and bottom
surface curvatures to promote the flow induced pressure difference that causes lift. The chord is defined
as the line connecting the leading edge and the trailing edge. Camber is defined as the maximum
distance from the chord to either surface. Chord length, , is the overall airfoil length. Angle of attack,
, is defined as the angle between the extended chord and the relative fluid flow direction (usually
horizontal).
Figure 2: Coefficient pressure distribution over an airfoil
Aerodynamic forces result from the pressure distribution over the surface. One useful way to evaluate
the aerodynamic forces is to use pressure taps to record the distribution and to integrate the
distribution to find the net force. For lift this integration is concerned with the pressure distribution in
the vertical direction, while for drag the horizontal pressure distribution is important. You can see from
the image how the surface “pushes back” with a force against the pressure, which always acts normal to
the surface. Surface curvature is IMPORTANT
Two mechanisms are used to generate Lift. The first is an asymmetric profile (about the chord – defined
in previous slide). This is often used for subsonic flight applications. The second is to incline the airfoil at
an angle relative to horizontal, which is usually the “relative wind angle”. For low values of this angle
(angle of attack) the flow remains attached on both surfaces. For higher angles of attack separation
occurs that increases drag and reduces lift. Eventually, the airfoil (and vehicle!) reaches a stall condition,
where the pressure distribution on the top and bottom are equal
Determining Aerodynamic Forces from a Pressure Distribution
As we have stated, one way to evaluate the aerodynamic forces is to measure the surface pressure
distribution and integrate that over the airfoil area. Pressure acts normal to the surface, so the
curvature must be known at the measurement location. NOTE that the angle relative to the wind
influences the pressure distribution. The total force the pressure distribution exerts on the wing is:
∙
(1)
We take that the wind is traveling in the x-direction. With this we can decompose the resultant force
into horizontal and vertical components to recover the aerodynamic forces of lift and drag:
cos
(2)
sin
(3)
To handle different wind conditions, non-dimensional (unitless!) representations are used based on the
pressure coefficient:
!
1
$ ( )
2 %&' !
*!
*!
!
1
$ ( )
2 %&' !
(4)
(5)
is the difference between local static pressure and free-stream (at ∞) static pressure, nondimensionalized by the free-stream dynamic pressure. What does an airfoil pressure coefficient
vs. -/ .
distribution look like? We generally plot
Figure 3: Coefficient pressure distribution over an airfoil
at the airfoil stagnation point is unity. Why is this? Think of Bernoulli relation and definition of the
stagnation point (/01%2 0). It then rapidly decreases on both the upper and lower surfaces and finally
recovers to a small positive value of 4 near the trailing edge. The upper surface pressure is lower
(plotted higher on the usual scale) than the lower surface
in this case… but it doesn't have to be. The
lower surface sometimes carries a positive pressure, but at many design conditions is actually pulling the
wing downward. The pressure at the trailing edge is related to the airfoil thickness and shape near the
trailing edge. Large positive values of 4 at the trailing edge imply more severe adverse pressure
gradients. Pressure recovery region: Pressure increases from its minimum value to the value at the
trailing edge. This adverse pressure gradient is associated with boundary layer transition and possibly
separation, if the gradient is too severe… which occurs at higher angles of attack!!!
It is common to also common to represent Lift and Drag non-dimensionally (no units!) as the Lift and
Drag coefficient:
*! 5
*! 5
(6)
(7)
Here 5 is the wing planform area which represents the viewed area of the wing from a top view (see
Figure 4). The contribution of wing curvature to the total wetted area of the wing is not needed for the
above lift and drag coefficient calculations.
Figure 4: Wing planform illustration
Figure 5 represents lift and drag coefficients for a NACA 4412 airfoil section at various angles of attack
and Reynolds numbers. The upper-left plot represents lift coefficient vs. angle of attack and shows a
common important trend where the lift, as expected, increases with angle of attack. At some point,
however, this lift reduces dramatically after a certain angle of attack. The angel where peak lift occurs is
referred to the critical angle of attack. This is a point where the flow separation on the upper surface of
the airfoil (caused by a large adverse pressure gradient) is large enough to begin to decrease the overall
lift of the aerodynamic surface.
Figure 5: Lift and drag coefficients for a NACA 4412 airfoil section.
2. Experimental Arrangement
This experiment will again make use of the Flowtek 1440 low speed wind tunnel with a 1’x1’ test section
(Figure 6).
Figure 6: Flowtek 1440 low-speed 1’x1’ wind tunnel.
The rectangular wing used for this lab has a NACA 2415 airfoil section with a chord length of _____ m
and a span of _____ m. This wing section is outfitted with eight upper surface pressure taps and eight
lower surface taps and six one-inch long tufts for flow separation visualization (see Figure 7). Relevant
pressure tap data can be found in Table 1 and Table 2.
Figure 7: Wing section with NACA 2415 airfoil.
Pressure is to be calculated from recorded manometer height measurements. The manometer is using
water as a working fluid ($6 = 1000 kg/m3).
Table 1: NACA 2415 upper surface pressure tap location data
Pressure Tap
Leading Edge
1
2
3
4
5
6
7
8
Trailing Edge
7 (%c)
0
1.193
5.688
14.89
25.40
39.44
54.25
68.64
84.16
100
8 (%c)
0
2.657
5.374
7.944
9.185
9.278
8.155
6.308
3.628
0
9 [rad]
:; [m2]
0.9006
0.3688
0.1838
0.05831
-0.03975
-0.1037
-0.1503
-0.2111
0.002577
0.003374
0.004548
0.00561
0.006633
0.006633
0.006785
0.01107
Table 2: NACA 2415 upper surface pressure tap location data
Pressure Tap
Leading Edge
9
10
11
12
13
14
15
16
Trailing Edge
7 (%c)
0
8 (%c)
0
9 [rad]
:; [m2]
1.451
6.730
14.11
21.70
35.08
49.93
63.99
80.72
100
-2.213
-4.301
-5.353
-5.688
-5.467
-4.673
-3.585
-2.083
0.7282
0.7282
0.08516
0.00835
-0.03805
-0.06709
-0.08428
-0.1027
0.002502
0.002994
0.003411
0.00474
0.006444
0.006595
0.00705
0.01251
0
3. Measurements
•
•
•
•
•
•
•
Experiment will make use of a NACA 2415 airfoil mounted into the Flowtek 1440 1’x1’ wind
tunnel
Start the wind tunnel
Set the desired angle of attack and adjust the RPM to obtain the desired upstream air velocity,
(! (consult your data from the Venturi lab)
Record the pressure readings for the 16 taps
Rotate airfoil and readjust speed.
Determine the airfoil stall angle for both positive and negative angle
Use tufts as a visual tool for stall.
For each angle and wind speed setting you are required to record manometer heights for the
! location, the atmospheric pressure (recall from the Venturi lab that this is the total pressure), and
the 16 airfoil surface pressures.
You will take measurements at one wind speed over a range of angle of attack. At this given wind speed,
adjust the airfoil to notice when full stall occurs. Your range of angle of attacks will proceed from a
negative angle of attack in sufficient steps until this stall angle is reached. One example would be to
start at about negative 6 degrees. Using about 10 steps, for example, if you visualize the stall angle at
positive 14 degrees, then you will march your measurements in about 20/10 degree increments (of
course logically round this value off to fit with the scale of the protractor).
4. Reduction of Data
Recall that the wind tunnel has a reference pressure tap located upstream of the test section on the
tunnel wall. The pressure at this location can be found from the following relation:
$6%1<' = >%1?
!
>!
(8)
From the Bernoulli relation we can find the corresponding velocity at the inlet:
2$6%1<' = >%1?
@
$%&'
(!
>!
(9)
The 16 pressure taps provide pressure values determined from the manometer as:
&
ABC
$6%1<' = >%1?
>&
The resulting pressure coefficient acting on each panel can be found from:
D
&
*!
!
(4)
Recall the total force the pressure distribution exerts on the wing is represented as a total surface
integral. As we do not have a continuous pressure distribution we evaluate this with a numerical
summation.
Figure 8: Wing planform illustration
Taking account of both the angle of the surface normal relative to the chord normal at each tap and the
angle of attack, the force evaluation in the vertical direction is the lift force:
E
&
&
cos
&
F
&
&
F
&
A similar expression can be derived for the drag force:
E
&
&
sin
5. Analysis and Discussion for Report
5.1) Lift and Drag
For a set airspeed you are to compare lift vs. angle of attack and to discuss stall characteristics of the
airfoil at that airspeed. You will do this for multiple airspeeds. Thus you will need to determine the lift
and drag coefficients for various air speeds and angles of attack.
5.2) Pressure Distribution and Stall
For one airspeed you will also determine the pressure coefficient distribution over the airfoil for various
angles of attack. Show how the 4 distribution changes as the angle of attack increases and discuss
what you see happening as the airfoil transitions to a state of stall.
5.3) Comparison with LIterature
You must compare your data with existing literature and show that your results make sense. One of the
first standard resources regarding airfoil data presents plenty of data at Reynolds numbers of 3x106 and
higher [5]. However, your experimental conditions will present lower Reynolds numbers than this. You
are required to determine your Reynolds numbers and to research and find relevant airfoil data (lift and
drag coefficient vs. angle of attack) near these Reynolds number values.
5.4) Uncertainty and Sensitivity Analysis
As usual, an uncertainty analysis is required of all relevant measurements. This includes an adequate
sensitivity analysis to show where largest sources of error arise.
6. References
[1] F. M. White, “Fluid Mechanics,” McGraw Hill, 2008.
[2] F. M. White, “Viscous Fluid Flow,” 3rd Edition, McGraw Hill, 2006.
[3] J.D. Anderson, “Fundamentals of Aerodynamics”,
[4] Kuethe and Chow, “Foundations of Aerodynamics: Bases of Aerodynamic Design,” 4th edition,
John Wiley and Sons, 1986
[5] Abbott and von Doenhoff, “Theory of Wing Sections: Including a Summary of Airfoil Data,”